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Feminism is fashionable. That's the statement we are never supposed to utter, within earshot of either feminists or fashion editors.<br><br>That's because feminists understandably rail against the co-opting of their cause as a "trend", while editors, the press and some fashion designers rankle at the [https://www.google.com/search?hl=en&gl=us&tbm=nws&q=implication&btnI=lucky implication] that their brave stance for womankind is viewed on a par with the ensemble cast of Sex and the City 2 performing Helen Reddy's empowering 1971 anthem "I Am Woman".<br><br>But feminism is fashionable, insomuch as it is being name-checked by the fashion industry with a striking frequency. Miuccia Prada's spring/summer 2014 collection was based on "the multiplicity of guises that women assume in the course of a day, a lifetime", a notion interpreted by many as fundamentally feminist.<br>For once, however, this feeling didn't start with Miuccia Prada: over the past few years, any female fashion designer or editor seems to be asked their views on the topic. Collections by every designer from Donatella Versace, to Phoebe Philo at C�line, to the London duo Meadham Kirchhoff, have been interpreted as feminist - whether the designers intended it or not.<br><br>Last November, British Elle began a campaign to "rebrand" feminism, inviting feminist publications Vagenda and Feminist Times to work with advertising agencies to rework the terminology.<br>Prada spring/summer 2014 fashion show <br>"What we did was ask, 'Does the word need rebranding?' The only thing that seemed an issue was the word," says Lorraine Candy, Elle's editor-in-chief. "We just asked a question." The response to Elle's question was staggering: a reach of 135 million on Twitter for the campaign, which Candy emphasises "is the biggest thing we've had engagement in, on Twitter, it's extraordinary� I was slightly taken aback by the force of opinion, the need from young women to talk about it� It struck me that this is a debate that everyone is having at the moment," Candy state<br><br>
'''Mertens stability''' is a [[solution concept]] used to predict the outcome of a non-cooperative game. A tentative definition of stability was proposed by Elon Kohlberg and [[Jean-François Mertens]]<ref>{{cite journal|authors=Kohlberg, Elon, and Jean-François Mertens|year=1986|title=On the Strategic Stability of Equilibria|journal=Econometrica|volume=54|issue=5|pages=1003–1037|jstor=1912320|url=http://www.dklevine.com/archive/refs4445.pdf}}</ref> for games with finite numbers of players and strategies. Later, Mertens<ref>Mertens, Jean-François, 1989, and 1991. "Stable Equilibria - A Reformulation," Mathematics of Operations Research, 14: 575-625 and 16: 694-753. [http://www.jstor.org/pss/3689732]</ref> proposed a stronger definition that was elaborated further by Srihari Govindan and Mertens.<ref>Govindan, Srihari, and Jean-François Mertens, 2004. "An Equivalent Definition of Stable Equilibria," International Journal of Game Theory, 32(3): 339-357. [http://www.springerlink.com/content/tjue9agca1l7qy87/] [http://hdl.handle.net/10.1007/s001820400165]</ref> This solution concept is now called [[Mertens stability]], or just stability.
"If you look at women's magazines in the last year, you'll see the word being used more than I think it ever has been<br>
In itself, this was the motivation for Elle to tackle the terminology head-on. "I feel it excludes younger women," says Candy. "Younger women felt they wouldn't know enough to be a feminist, if you haven't read Germaine Greer or Marilyn French� I think there is still a lot of confusion around it, and I think the word remains quite contentiou<br><br>


Elle sought to unpick the meaning behind the word, rather than just splashing it across its front-page. However, the issue with feminism in fashion for some is exactly that: the use of the term for simple, superficial sloganeering. "It absolutely has become a buzzword," says Reni Eddo-Lodge, a journalist and contributing editor to the website Feminist Times, "and a lot of the time there is a lot of confusion about what it means. There isn't a huge, joined-up movement like there was 30 or 40 years ago. There's no agreement." For Eddo-Lodge, this is an enormous iss<br><br>
Like other refinements of [[Nash equilibrium]]<ref>Govindan, Srihari & Robert Wilson, 2008. "Refinements of Nash Equilibrium," The New Palgrave Dictionary of Economics, 2nd edition. [http://myweb.uiowa.edu/sgovinda/Working-Papers/Refinements%20of%20Nash%20equilibrium-Palgrave-Govindan%20and%20Wils%E2%80%A6.pdf]</ref>
used in [[game theory]] stability selects subsets of the set of Nash equilibria that have desirable properties. Stability invokes stronger criteria than other refinements, and thereby ensures that more desirable properties are satisfied.


"The word is meaningless if there are no politics to back it up� Ultimately feminism is a political moveme<br>."
==Desirable Properties of a Refinement==
Politics are often rinsed from fashionable feminism. It's understandable: fashion is primarily visual, so aesthetic elements do the talking, unless you're literally sloganeering, in the manner of Katharine Hamnett in the 1980s. "This collection really became about female power," said the jewellery designer Eddie Borgo of his spring 2014 collection. "It gives [women] strength." The collection could easily have been interpreted as punk, with its zip-teeth and razor-sharp ed<br><br>


But punk is very 2013. Generally, designers scrabble after the same grab-bag of "feminist" signifiers: clich�s of the "tough woman" or "power dressing," big shoulders, high heels, zips and studs. "Some people consider feminism to be climbing into the boardroom, becoming Sheryl Sandberg," says Eddo-Lo<br>e.
Refinements have often been motivated by arguments for admissibility, backward induction, and forward induction. In a two-player game, an [[admissible decision rule]] for a player is one that does not use any strategy that is weakly dominated by another (see [[Strategic dominance]]). [[Backward induction]] posits that a player's optimal action in any event anticipates that his and others' subsequent actions are optimal. The refinement called [[subgame perfect equilibrium]] implements a weak version of backward induction, and increasingly stronger versions are [[sequential equilibrium]], [[perfect equilibrium]], [[quasi-perfect equilibrium]], and [[proper equilibrium]]. [[Forward induction]] posits that a player's optimal action in any event presumes the optimality of others' past actions whenever that is consistent with his observations. Forward induction<ref>Govindan, Srihari, and Robert Wilson, 2009. "On Forward Induction," Econometrica, 77(1): 1-28. [http://onlinelibrary.wiley.com/doi/10.3982/ECTA6956/abstract] [http://onlinelibrary.wiley.com/doi/10.3982/ECTA6956/pdf]</ref> is satisfied by a sequential equilibrium for which a player's belief at an information set assigns probability only to others' optimal strategies that enable that information to be reached.
"Feminism for me is about liberation from structural power." That's much more difficult to evoke in a skirt-s<br>t.
Other designers' work can be more unexpectedly interpreted as feminist: the fact that JW Anderson cross-pollinates the wardrobes of men and women, for instance, to the extent that he cut his winter 2013 menswear trousers without a phallocentric masculine bu<br><br>


He may not approach fashion with a strictly feminist intent, but it is easy to interpret Anderson's clothes as such. The same is true of Phoebe Philo, arguably the spark that ignited the feminism and [http://Www.Dailymail.Co.uk/home/search.html?sel=site&searchPhrase=fashion+debate fashion debate]. She left her previous role at Chlo� to focus on her personal life, and moved the C�line studio to London when she took over the house's reins in <br><br>.
Kohlberg and Mertens emphasized further that a solution concept should satisfy the ''invariance'' principle that it not depend on which among the many equivalent representations of the strategic situation as an [[extensive-form game]] is used. Thus it should depend only on the reduced [[normal-form game]] obtained after elimination of pure strategies that are redundant because their payoffs for all players can be replicated by a mixture of other pure strategies. Mertens<ref>Mertens, Jean-François, 2003. "Ordinality in Non Cooperative Games," International Journal of Game Theory, 32: 387–430. [http://www.springerlink.com/content/qnggpw13qw8c4v9m/]</ref><ref>Mertens, Jean-François, 1992. "The Small Worlds Axiom for Stable Equilibria," Games and Economic Behavior, 4: 553-564. [http://www.sciencedirect.com/science/article/pii/089982569290036R]</ref> emphasized also the importance of the ''small worlds'' principle that a solution concept should depend only on the ordinal properties of players' preferences, and should not depend on whether the game includes extraneous players whose actions have no effect on the original players' feasible strategies and payoffs.


Celine's designer, Pheobe <br>ilo
Kohlberg and Mertens demonstrated via examples that not all of these properties can be obtained from a solution concept that selects single Nash equilibria. Therefore, they proposed that a solution concept should select closed connected subsets of the set of Nash equilibria.<ref>The requirement that the set is connected excludes the trivial refinement that selects all equilibria. If only a single (possibly unconnected) subset is selected then only the trivial refinement satisfies the conditions invoked by H. Norde, J. Potters, H. Reijnierse, and D. Vermeulen (1996): ``Equilibrium Selection and Consistency,'' Games and Economic Behavior, 12: 219-225.</ref>
"One of the things we share is the reality that the clothes we design are actually worn," says fellow designer Stella McCartney about Philo's output. That reality of dressing working women with a sense of the practical, as well as the fashionable, is often seen as femi<br><br>.


"The flat shoe has been a big trend," adds Candy. "Those cripplingly high shoes aren't coming through anymore. Maybe it's a subconscious thing - of just being nicer to women!" What could be more feminist than <br>at?
==Properties of Stable Sets==
My own issues with feminism and  [http://www.pcs-systems.co.uk/Images/celinebag.aspx http://www.pcs-systems.co.uk/Images/celinebag.aspx] fashion are simple: fashion is an industry, and feminism, as Eddo-Lodge succinctly puts it, is a political movement with distinct aims for equality between the sexes. The trouble with tying such noble aims to fashion is that it can look like you're trying to tug on heartstrings to hawk somet<br><br>.


"As a fashion magazine, a lot of criticism around us was 'How dare you engage with this?' - given that a lot of what we do is about make-up, and nail polish and handbags," says Candy of Elle's rebranding campaign. "How could we say that when we place so much emphasis on how women look? But how women look is incredibly important to their day-to-day li<br>s."
* Admissibility and Perfection: Each equilibrium in a stable set is perfect, and therefore admissible.
Activists of the feminist movement FEMEN protest on the catwalk as models present creations for Nina Ricci during the 2014 Spring/Summer ready-to-wear collection fashion <br><br>


Some argue that simply raising the profile of the word, and stimulating discussion of feminism in popular culture, is valuable enough. Eddo-Lodge has other feelings. "Wishy-washy awareness-raising is good, but it almost adds to the confusion. What does it mean? What are the politics behind it?" But for Candy, engagement with the "Rebranding Feminism" campaign has fundamentally altered the way she w<br>ks.
* Backward Induction and Forward Induction: A stable set includes a proper equilibrium of the normal form of the game that induces a quasi-perfect and therefore a sequential equilibrium in every extensive-form game with perfect recall that has the same normal form. A subset of a stable set survives iterative elimination of weakly dominated strategies and strategies that are inferior replies at every equilibrium in the set.
"Are we patronising women? Are we doing things that are accidentally sexist? Are we writing in the right language?" These are questions she throws out to herself, rather than at the world at l<br><br>.


There is even an argument that the mere act of embracing the fashion industry is intrinsically feminist. "Feminine things like fashion and beauty are often considered less worthy pursuits," reasons Eddo-Lodge. "Some feminists talk about 'fem phobia', of heaping disgust on things that are seen as traditionally feminine, so in a way I think embracing fashion can be hugely liberating for women and men." That's a resolutely modern idea of feminism: "I was a feminist in the sixties," stated Miuccia Prada in <br><br>.
* Invariance and Small Worlds: The stable sets of a game are the projections of the stable sets of any larger game in which it is embedded while preserving the original players' feasible strategies and payoffs.<ref>See Appendix D of Govindan, Srihari, and Robert Wilson, 2012. "Axiomatic Theory of Equilibrium Selection for Generic Two-Player Games," Econometrica, 70. [https://gsbapps.stanford.edu/researchpapers/library/RP2021R.pdf]</ref>


"Can you imagine? The worst thing I could have done was to be in fashion." Not any more.
* Decomposition and Player Splitting.  The stable sets of the product of two independent games are the products of their stable sets. Stable sets are not affected by splitting a player into agents such that no path through the game tree includes actions of two agents.
 
For two-player games with perfect recall and generic payoffs, stability is equivalent to just three of these properties: a stable set uses only undominated strategies, includes a quasi-perfect equilibrium, and is immune to embedding in a larger game.<ref>Govindan, Srihari, and Robert Wilson, 2012. "Axiomatic Theory of Equilibrium Selection for Generic Two-Player Games," Econometrica, 70. [https://gsbapps.stanford.edu/researchpapers/library/RP2021R.pdf]</ref>
 
==Definition of a Stable Set==
 
A stable set is defined mathematically by essentiality of the projection map from a closed connected neighborhood in the graph of the Nash equilibria over the space of perturbed games obtained by perturbing players' strategies toward completely mixed strategies. This definition requires more than every nearby game having a nearby equilibrium. Essentiality requires further that no deformation of the projection maps to the boundary, which ensures that perturbations of the fixed point problem defining Nash equilibria have nearby solutions. This is apparently necessary to obtain all the desirable properties listed above.
 
Mertens provided several formal definitions depending on the coefficient module used for homology or cohomology.
 
A formal definition requires some notation. For a given game <math>G</math> let <math>\Sigma</math> be product of the simplices of the players' of mixed strategies. For each <math>0 < \delta \le 1</math>, let <math>P_\delta = \{\,\epsilon\tau \mid 0 \le \epsilon \le \delta,\tau \in \Sigma\,\}</math> and let <math>\partial P_\delta</math> be its topological boundary. For <math>\eta \in P_{1}</math> let <math>\bar{\eta}</math> be the minimum probability of any pure strategy. For any <math>\eta \in P_1</math> define the perturbed game <math>G(\eta)</math> as the game where the strategy set of each player <math>n</math> is the same as in <math>G</math>, but where the payoff from a strategy profile <math>\tau</math> is the payoff in <math>G</math> from the profile <math>\sigma = (1-\bar{\eta})\tau + \eta</math>. Say that <math>\sigma</math> is a perturbed equilibrium of <math>G(\eta)</math> if <math>\tau</math> is an equilibrium of <math>G(\eta)</math>. Let <math>\mathcal{E}</math> be the graph of the perturbed equilibrium correspondence over <math>P_1</math>, viz., the graph <math>\mathcal{E}</math> is the set of those pairs <math>(\eta,\sigma) \in P_1 \times \Sigma</math> such that <math>\sigma</math> is a perturbed equilibrium of <math>G(\eta)</math>. For <math>(\eta,\sigma) \in \mathcal{E}</math>, <math>\tau(\eta,\sigma) \equiv (\sigma - \eta)/(1-\bar{\eta})</math> is the corresponding equilibrium of <math>G(\eta)</math>. Denote by <math>p</math> the natural projection map from <math>\mathcal{E}</math> to <math>P_1</math>. For <math>E \subseteq \mathcal{E}</math>, let <math>E_0 = \{\, (0, \sigma) \in E \, \}</math>, and for <math>0 < \delta \le 1</math> let <math>(E_\delta,\partial E_\delta) = p^{-1}(P_\delta,\partial P_\delta) \cap E</math>. Finally, <math>\check{H}</math> refers to Čech cohomology with integer coefficients.
 
The following is a version of the most inclusive of Mertens' definitions, called *-stability.
 
'''''Definition of a *-stable set''''': <math>S \subseteq \Sigma</math> is a *-stable set if for some closed subset <math>E</math> of <math>\mathcal{E}</math> with <math>E_0 = \{\, 0 \,\} \times S</math> it has the following two properties:
 
* '''Connectedness''': For every neighborhood <math>V</math> of <math>E_0</math> in <math>E</math>, the set <math>V \setminus \partial E_1</math> has a connected component whose closure is a neighborhood of <math>E_0</math> in <math>E</math>.
 
* '''Cohomological Essentiality''': <math>p^*: \check{H}^*(P_\delta,\partial P_\delta) \to \check{H}^*(E_\delta, \partial E_\delta)</math> is nonzero for some <math>\delta > 0</math>.
 
If essentiality in cohomomology or homology is relaxed to homotopy then a weaker definition is obtained, which differs chiefly in a weaker form of the decomposition property.<ref>Srihari Govindan and Robert Wilson, 2008. "Metastable Equilibria," Mathematics of Operations Research, 33: 787-820.</ref>
 
== References ==
{{reflist|30em}}
{{refend}}
{{game theory}}
 
[[Category:Game theory]]

Revision as of 01:44, 2 June 2013

Mertens stability is a solution concept used to predict the outcome of a non-cooperative game. A tentative definition of stability was proposed by Elon Kohlberg and Jean-François Mertens[1] for games with finite numbers of players and strategies. Later, Mertens[2] proposed a stronger definition that was elaborated further by Srihari Govindan and Mertens.[3] This solution concept is now called Mertens stability, or just stability.

Like other refinements of Nash equilibrium[4] used in game theory stability selects subsets of the set of Nash equilibria that have desirable properties. Stability invokes stronger criteria than other refinements, and thereby ensures that more desirable properties are satisfied.

Desirable Properties of a Refinement

Refinements have often been motivated by arguments for admissibility, backward induction, and forward induction. In a two-player game, an admissible decision rule for a player is one that does not use any strategy that is weakly dominated by another (see Strategic dominance). Backward induction posits that a player's optimal action in any event anticipates that his and others' subsequent actions are optimal. The refinement called subgame perfect equilibrium implements a weak version of backward induction, and increasingly stronger versions are sequential equilibrium, perfect equilibrium, quasi-perfect equilibrium, and proper equilibrium. Forward induction posits that a player's optimal action in any event presumes the optimality of others' past actions whenever that is consistent with his observations. Forward induction[5] is satisfied by a sequential equilibrium for which a player's belief at an information set assigns probability only to others' optimal strategies that enable that information to be reached.

Kohlberg and Mertens emphasized further that a solution concept should satisfy the invariance principle that it not depend on which among the many equivalent representations of the strategic situation as an extensive-form game is used. Thus it should depend only on the reduced normal-form game obtained after elimination of pure strategies that are redundant because their payoffs for all players can be replicated by a mixture of other pure strategies. Mertens[6][7] emphasized also the importance of the small worlds principle that a solution concept should depend only on the ordinal properties of players' preferences, and should not depend on whether the game includes extraneous players whose actions have no effect on the original players' feasible strategies and payoffs.

Kohlberg and Mertens demonstrated via examples that not all of these properties can be obtained from a solution concept that selects single Nash equilibria. Therefore, they proposed that a solution concept should select closed connected subsets of the set of Nash equilibria.[8]

Properties of Stable Sets

  • Admissibility and Perfection: Each equilibrium in a stable set is perfect, and therefore admissible.
  • Backward Induction and Forward Induction: A stable set includes a proper equilibrium of the normal form of the game that induces a quasi-perfect and therefore a sequential equilibrium in every extensive-form game with perfect recall that has the same normal form. A subset of a stable set survives iterative elimination of weakly dominated strategies and strategies that are inferior replies at every equilibrium in the set.
  • Invariance and Small Worlds: The stable sets of a game are the projections of the stable sets of any larger game in which it is embedded while preserving the original players' feasible strategies and payoffs.[9]
  • Decomposition and Player Splitting. The stable sets of the product of two independent games are the products of their stable sets. Stable sets are not affected by splitting a player into agents such that no path through the game tree includes actions of two agents.

For two-player games with perfect recall and generic payoffs, stability is equivalent to just three of these properties: a stable set uses only undominated strategies, includes a quasi-perfect equilibrium, and is immune to embedding in a larger game.[10]

Definition of a Stable Set

A stable set is defined mathematically by essentiality of the projection map from a closed connected neighborhood in the graph of the Nash equilibria over the space of perturbed games obtained by perturbing players' strategies toward completely mixed strategies. This definition requires more than every nearby game having a nearby equilibrium. Essentiality requires further that no deformation of the projection maps to the boundary, which ensures that perturbations of the fixed point problem defining Nash equilibria have nearby solutions. This is apparently necessary to obtain all the desirable properties listed above.

Mertens provided several formal definitions depending on the coefficient module used for homology or cohomology.

A formal definition requires some notation. For a given game G let Σ be product of the simplices of the players' of mixed strategies. For each 0<δ1, let Pδ={ϵτ0ϵδ,τΣ} and let Pδ be its topological boundary. For ηP1 let η¯ be the minimum probability of any pure strategy. For any ηP1 define the perturbed game G(η) as the game where the strategy set of each player n is the same as in G, but where the payoff from a strategy profile τ is the payoff in G from the profile σ=(1η¯)τ+η. Say that σ is a perturbed equilibrium of G(η) if τ is an equilibrium of G(η). Let be the graph of the perturbed equilibrium correspondence over P1, viz., the graph is the set of those pairs (η,σ)P1×Σ such that σ is a perturbed equilibrium of G(η). For (η,σ), τ(η,σ)(ση)/(1η¯) is the corresponding equilibrium of G(η). Denote by p the natural projection map from to P1. For E, let E0={(0,σ)E}, and for 0<δ1 let (Eδ,Eδ)=p1(Pδ,Pδ)E. Finally, Hˇ refers to Čech cohomology with integer coefficients.

The following is a version of the most inclusive of Mertens' definitions, called *-stability.

Definition of a *-stable set: SΣ is a *-stable set if for some closed subset E of with E0={0}×S it has the following two properties:

  • Connectedness: For every neighborhood V of E0 in E, the set VE1 has a connected component whose closure is a neighborhood of E0 in E.

If essentiality in cohomomology or homology is relaxed to homotopy then a weaker definition is obtained, which differs chiefly in a weaker form of the decomposition property.[11]

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro. Template:Refend Earlier than you decide whether stainless steel cookware is worth buying, lets first discuss what stainless steel cookware is. Chrome steel is manufactured from an alloy, or a mix of metals. Mostly, basic iron with chromium, nickel or another minor metals. The chromium supplies rust safety and gives your cookware durability. The nickel supplies rust safety as effectively, and adds a elegant look. Most properly made chrome steel cookware has copper or aluminum added to the bottom of the pan or pot. That is performed to increases the ability of the pot or pan to conduct heat.
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    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  2. Mertens, Jean-François, 1989, and 1991. "Stable Equilibria - A Reformulation," Mathematics of Operations Research, 14: 575-625 and 16: 694-753. [1]
  3. Govindan, Srihari, and Jean-François Mertens, 2004. "An Equivalent Definition of Stable Equilibria," International Journal of Game Theory, 32(3): 339-357. [2] [3]
  4. Govindan, Srihari & Robert Wilson, 2008. "Refinements of Nash Equilibrium," The New Palgrave Dictionary of Economics, 2nd edition. [4]
  5. Govindan, Srihari, and Robert Wilson, 2009. "On Forward Induction," Econometrica, 77(1): 1-28. [5] [6]
  6. Mertens, Jean-François, 2003. "Ordinality in Non Cooperative Games," International Journal of Game Theory, 32: 387–430. [7]
  7. Mertens, Jean-François, 1992. "The Small Worlds Axiom for Stable Equilibria," Games and Economic Behavior, 4: 553-564. [8]
  8. The requirement that the set is connected excludes the trivial refinement that selects all equilibria. If only a single (possibly unconnected) subset is selected then only the trivial refinement satisfies the conditions invoked by H. Norde, J. Potters, H. Reijnierse, and D. Vermeulen (1996): ``Equilibrium Selection and Consistency, Games and Economic Behavior, 12: 219-225.
  9. See Appendix D of Govindan, Srihari, and Robert Wilson, 2012. "Axiomatic Theory of Equilibrium Selection for Generic Two-Player Games," Econometrica, 70. [9]
  10. Govindan, Srihari, and Robert Wilson, 2012. "Axiomatic Theory of Equilibrium Selection for Generic Two-Player Games," Econometrica, 70. [10]
  11. Srihari Govindan and Robert Wilson, 2008. "Metastable Equilibria," Mathematics of Operations Research, 33: 787-820.